Relaxation labeling processes for the traveling salesman problem

Relaxation labeling processes are a class of parallel distributed processing models developed to reduce local ambiguities and achieve global consistency in labeling problems. They have become a standard technique in the computer vision domain, and possess certain common properties with both artificial and biological neural systems. In particular, like the Hopfield network, they have a quadratic Lyapunov function when a symmetry condition is satisfied. In this paper the use of relaxation processes to solve the traveling salesman problem is proposed and it is quantitatively demonstrated that the algorithm is extremely effective both in finding legitimate problem solutions and in discovering optimal tours.